I am usually still in the kitchen preparing the rest of the meal by the time the alarm rings, so turning off the stove is not a big inconvenience.
There's also another advantage of the instant pot method: because it's cooking under pressure, it compresses the whites very slightly inside the shells as they cook. This means the shells always peel very easily from the eggs! Often when stovetop cooking, I'd get the shells sticking to the eggs which makes them difficult to peel.
But it's not the end of the world if you don't as it cools down quite quickly when it vents (if set to quick-release). They might be slightly overdone, but certainly not as bad as forgetting them and leaving them boiling in a pot for 15+ minutes. Which I've done more times than I care to admit.
I usually make boiled eggs when I take food somewhere (be it for hiking or a lunch in the park). But I also drop them into cold water once they are cooked to stop the cooking, so they are quickly not that hot anymore.
Not having to worry about the timing does sound nice!
With a stove top method, you have to stand there and watch the timer, and manually turn off your stove when it's done.